Q$.3(\%20)$ The following parameters are given for a single phase weaving machine $($assuming the efficiency of the machine is $80\%)$; The speed of the main shaft is $900$ rpm $,$ The fabric width is $240$ cm $,$ The weft sett $($pich density$)$ is $30$ ppc $.$ If the rapier can be made to enter the shed at $60$ and leave at $300.$

a$.)$ Calculate the productivity of the given machine in terms of square meters of fabric produced

b$.)$ Calculate the average speed of the rapier with yarn in metre$/$second$.$